Linear estimation techniques may be expanded to approximate solutions to non-linear systems through the use of kernelization functions. These non-linear functions may be utilized to map input signals of a non-linear system in order to produce a set of kernels. The output signals of the system may subsequently be assumed to be a linear function of the resulting kernels, thereby allowing for the use of conventional linear estimation techniques in order to realize a comprehensive system model.
The estimation of non-linear systems may be of interest in a variety of real world scenarios. Electronic applications may be of particular relevance, such as the non-linear relationships characterizing voltage and power through resistive components, oversaturated amplification components, digital logic devices, electronic distortion, etc.
Once obtained, solutions to these non-linear systems may be applied in order to improve device performance. One such application is the cancellation of leakage signals in for wireless transceiver devices susceptible to self-interference, where signals transmitted by the transmit chain leak into the receive chain, thereby introducing interference into received signals. The associated interference may be effectively mitigated and/or canceled by approximating the signal path between the transmit chain and the receive chain, thereby obtaining a model characterizing the relationship between transmit signals transmitted by the transmit chain and resulting leakage signals contained in the received signal at the receive chain.
A variety of classical linear estimation techniques, such as linear mean square (LMS) or recursive least square (RLS), may then be applied in order to approximate a solution modeling the substantially linear relationship between the kernels and the leakage signal.